Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F₂ generation and subsequently among DH lines derived from the selected F₂ individual (Method 1), (2) MAS for augmented F₂ enrichment and subsequently for T among DH lines from the best carrier F₂ individual (Method 2), and (3) MAS for T among DH lines derived from the F₁ generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F₂ ( n₁^* \, n_{1}^{*} ) and DH generations (n - n₁^* ) (n - n_{1}^{*} ) for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F₂ individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F₂ individuals than DH lines ($ n_{1}^{*} :n > 0.5 $ n_{1}^{*} :n > 0.5 ), whereas under Method 2, the optimal ratio n₁^* :n n_{1}^{*} :n was close to 0.5. However, for ratios deviating moderately from the optimum, the mean `(X)] \overline{X} of T in the finally selected DH line ( T<sub>\textDH</sub><sup>*</sup> T_{\text{DH}}^{*} ) was hardly reduced. Method 3 had always the lowest mean `(X)] \overline{X} of T_\textDH^* T_{\text{DH}}^{*} except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean `(X)] \overline{X} and lowest SD of T_\textDH^* T_{\text{DH}}^{*} for the finally selected DH.